Question: If $a = 8$, what is the value of $\left(16\sqrt[3]{a^2}\right)^{\frac 13}$?
Explanation: Note that $a^2 = 64$ and $\sqrt[3]{64} = 4$. Therefore, $$\left(16\sqrt[3]{a^2}\right)^{\frac {1}{3}} = \left(16 \times 4\right)^{\frac{1}{3}} = 64^\frac{1}{3} = \boxed{4}.$$